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A Uniform Space–Time Gridding Algorithm for Comparison of Satellite Data Products:
Characterization and Sensitivity Study
NADIA SMITH, W. PAUL MENZEL, AND ELISABETH WEISZ
Space Science and Engineering Center, University of Wisconsin—Madison, Madison, Wisconsin
ANDREW K. HEIDINGER
NOAA/NESDIS/Center for Satellite Applications and Research, Madison, Wisconsin
BRYAN A. BAUM
Space Science and Engineering Center, University of Wisconsin—Madison, Madison, Wisconsin
(Manuscript received 1 February 2012, in final form 20 July 2012)
ABSTRACT
To overcome the complexities associated with combining or comparing multisensor data, a statistical
gridding algorithm is introduced for projecting data from their unique instrument domain to a uniform space–
time domain. The algorithm has two components: 1) a spatial gridding phase in which geophysical properties
are filtered on the basis of a set of criteria (e.g., time of day or viewing angle) and then aggregated into nearestneighbor clusters as defined by equal-angle grid cells and 2) a temporal gridding phase in which daily statistics
are calculated per grid cell from which longer time-aggregate statistics are derived. The sensitivity of the
gridding algorithm is demonstrated using a month (1–31 August 2009) of level 2 Aqua/Moderate Resolution
Imaging Spectroradiometer (MODIS) cloud-top pressure (CTP) retrievals as an example. Algorithm sensitivity is tested for grid size, number of days in the definition of a time average, viewing angle, and minimum
number of observations per grid cell per day. The average CTP for high-level clouds from a number of
different polar-orbiting instruments are compared on a 18 3 18 global grid. With the data projected onto
a single grid, differences in CTP retrieval algorithms are highlighted. The authors conclude that this gridding
algorithm greatly facilitates the intercomparison of CTP (or any other geophysical parameter) and algorithms
in a dynamic environment. Its simplicity lends transparency to understanding the behavior of a given parameter and makes it useful for both research and operational use.
1. Introduction
Geophysical properties, such as atmospheric and
surface temperatures, water vapor, aerosols, and clouds,
have been retrieved operationally from satellite measurements in both geostationary (regional) and polar
(global) orbits for more than three decades. While this
potentially allows large-scale, long-term analysis, issues
arise when comparing measurements from different
time periods and sensors. Data combination and intercomparison efforts become difficult because of differences in technology, horizontal and vertical resolution,
Corresponding author address: Dr. Nadia Smith, Space Science
and Engineering Center, University of Wisconsin—Madison, 1225
W. Dayton St., Madison, WI 53706.
E-mail: nadia.smith@ssec.wisc.edu
DOI: 10.1175/JAMC-D-12-031.1
Ó 2013 American Meteorological Society
satellite overpass time, sampling frequency, and retrieval
algorithm design strategies, among others. These difficulties are especially acute in climate studies that rely on
decades of continuous global data records from a variety
of satellite sensors.
A number of approaches to enhance data continuity
exist. One is the creation of instrument-specific gridded
aggregates. Historically, georeferenced calibrated sensor measurements at native instrument resolution are
referred to as level 1B (L1B), the retrieved geophysical
properties at instrument resolution as level 2 (L2), and
the geophysical properties gridded and aggregated over
a time period as level 3 (L3). The latter is useful, not only
because of lower data volumes and improved data accessibility, but also as a statistical description of the retrieved properties. The Moderate Resolution Imaging
Spectroradiometer (MODIS) L3 product, for example,
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contains hundreds of statistical data records on a 18 3 18
grid of L2 properties, such as aerosols, water vapor,
clouds, and atmospheric profiles, in daily, 8-day, and
monthly time aggregates (King et al. 2003). With close to
1000 records, however, the monthly product can easily
become too cumbersome to work with. In addition, it
may still not meet all research needs because of the static
definition of grid size, time, and type of statistics, for
example, mean instead of mode. There is also the possibility that a reprocessing of the entire product series
becomes necessary as new knowledge on the statistical nature of a parameter (e.g., nonnormal behavior) is
gained. This is both costly and complicated. This said,
the MODIS L3 product is perhaps one of the most comprehensive to date.
Clouds play a major role in weather and climate patterns and are widely studied as indicators of change and
trends (Ramanathan et al. 1989; Liou et al. 1993). The
development of globally gridded cloud climatologies to
date is either multi- or single sensor cloud properties
sampled to a uniform grid. Cloud climatologies include,
but are not limited to, the International Satellite Cloud
Climatology Project (ISCCP; Schiffer and Rossow 1983),
the University of Wisconsin High Resolution Infrared
Radiometer Sounder (UW HIRS; Wylie and Menzel 1999;
Wylie et al. 2005), the Pathfinder Atmospheres-Extended
(PATMOS-x; Heidinger and Pavolonis 2009), the Television and Infrared Observation Satellite (TIROS)-N
Operational Vertical Sounder (TOVS) Path-B measurements (Stubenrauch et al. 2006), and another based
on TOVS (Susskind et al. 1997). While there may be
uniformity of data in a single climatology, the same
issues arise when comparing or combining different
climatologies. Limitations in temporal scope, lack of
transparency as well as consensus among research teams
on gridding requirements (pertaining to grid size, type of
statistic, time period, etc.) make data comparison efforts
problematic.
There are examples in the literature where these
stated problems are partly overcome by resampling different gridded cloud products to a common geographic
grid using interpolation or zonal statistics (e.g., Hou
et al. 1993; Wang and Rossow 1995; Jin et al. 1996;
Stubenrauch et al. 1999 a,b,c; Hahn et al. 2001; Pavolonis
and Key 2003; Thomas et al. 2004; Zhang et al. 2005).
However, resampling a statistical dataset to a different
space–time configuration introduces errors that are often untraceable in the final solution. Moreover, unknown
errors may incorrectly depict trends.
In this paper, we propose a different approach. Instead of focusing on the development of a static global
gridded data product, our goal is to develop a method
with which any georeferenced dataset (independent of
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source instrument) of land, ocean, or atmosphere, at any
level of processing (L1B/2), can be projected from its
nonuniform instrument domain to a uniform space–time
domain. As such, the gridded output is tailored to specific research needs, created for a user-defined (not
product-defined) length of time, from any suite of instruments relevant to the study. To be clear, we do not attempt in any way to criticize the strengths and weaknesses
of existing climatologies or propose the replacement of
L3 products in this paper. Our intent is simply to offer
a different approach to a long-standing problem.
The implementation of a gridding algorithm, as opposed to relying on static gridded products, has distinct
advantages: (i) any geophysical property of interest at
any level of processing can be projected to the space–time
grid; (ii) all research relevant data are subject to the same
set of filters and projected onto a common geographic
grid; (iii) there are no predefined limitations on the type of
parameter or statistic, grid size, time period, or number of
gridded properties—these are all user-defined; (iv) the algorithm can be run as research needs arise, thereby reducing the need to aggregate and store L3 products; and (v)
the algorithm is straightforward and transparent for application in both research and operational environments.
The gridding algorithm proposed here has two
components. First is the ‘‘space’’ gridding phase where
geophysical properties are filtered based on a set of criteria (e.g., time of day, viewing angle) and then aggregated into nearest-neighbor clusters as defined by
equal-angle grid cells. Second is the ‘‘time’’ gridding
phase where daily statistics are built per grid cell from
which longer time-aggregate statistics are derived.
The data used in this study are discussed in section 2.
The space–time gridding algorithm is described in section 3. For clarification, the gridding of L2 MODIS
cloud-top pressure (CTP) retrievals is used as an algorithm application example throughout. However, the
reader should bear in mind that CTP can be substituted
with any L1B/2 geophysical parameter. Sections 4a and
4b detail the approach adopted in this paper to characterize the space–time algorithm and test its sensitivities
to sample size. The latter is determined by gridcell size,
aggregate time period, and viewing angle limitations.
Discussion of results follows in section 4c and a comparison is made of CTP monthly gridded averages from
four polar-orbiting instruments in section 5. Conclusions are reached in section 6 followed by recommendations for future research.
2. Data
All data processed in this paper are for the time period
1–31 August 2009 and from instruments on polar-orbiting
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platforms that obtain near global coverage in approximately two days.
a. Multispectral imagers
The Advanced Very High Resolution Radiometer
(AVHRR) on Meteorological Operation-A (MetOp-A)
senses in three visible (VIS) to near-infrared (NIR) (0.5–
1.64 mm) and three IR spectral bands (3.55–12.5 mm).
The MetOp-A orbit has a local morning crossing time of
0930. AVHRR cloud properties are retrieved with the
PATMOS-x cloud retrieval algorithm (Heidinger and
Pavolonis 2009). Globally gridded PATMOS-x level 2
retrieval products are available on a 0.18 grid from the
Cooperative Institute for Meteorological Satellite Studies (CIMSS; online at cimss.ssec.wisc.edu/patmosx). The
PATMOS-x gridding algorithm employs nearest-neighbor
logic with the result that there is only one CTP retrieval per 0.18 3 0.18 grid cell with no statistical data
abstraction.
The MODIS on Aqua is sensing in 36 spectral bands
ranging from 0.6 to 14.2 mm. The Aqua platform has
a local afternoon crossing time of 1330 and is part of
the A-Train constellation of sensors, which include the
Cloud-Aerosol Lidar and Infrared Pathfinder Satellite
Observations (CALIPSO) and CloudSat. The operational 5-km level 2 cloud product (MYD06) is described
in the literature (King et al. 2003; Platnick et al. 2003;
Menzel et al. 2008). MODIS has a swath dimension of
2330 km with a viewing angle limit of 65.38. This results
in 406 level 2 pixels across track per scan line. The
characterization and sensitivity studies in this paper are
based on the MODIS level 2 cloud retrieval product
(version 5). Data are available from the National Aeronautics and Space Administration (NASA) Goddard
Space Flight Center’s level 1 and Atmosphere Archive
and Distribution System (LAADS; online at ladsweb.
nascom.nasa.gov).
b. Hyperspectral sounder
The Atmospheric Infrared Sounder (AIRS) is mounted on Aqua and measures emitted infrared radiation in
2378 spectral channels spanning the range from 3.7 to
15 mm (Aumann et al. 2003; Chahine et al. 2006). AIRS
and MODIS are thus coincident in time. The level 2 retrieval algorithm is described by Susskind et al. (2003).
AIRS radiance observations as well as the standard level
2 retrieval products (that include CTP retrievals along
with surface properties and the atmospheric profiles of
temperature and gases) are found at the NASA Goddard
Earth Sciences Data and Information Services Center
(GES DISC, available online at daac.gsfc.nasa.gov). AIRS
CTP retrievals are available at 45 km 3 45 km horizontal
resolution, or roughly 0.48 3 0.48. Unlike MODIS, AIRS
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has a viewing angle limit of 48.958. This together with the
reduced footprint size leaves 90 fields of view (FOV)
across track per scan line.
c. Lidar
The Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP; Winker et al. 2004, 2007), onboard the
CALIPSO, is also an A-Train instrument. Its local
crossing time lags 1–2 min behind that of Aqua. The
level 2 cloud-layer product constitutes vertical profiles
of clouds retrieved at 5-km resolution. However, unlike
the passive sensors, there is only a single footprint across
track. A strong advantage of CALIOP is that it has a
very high vertical resolution of 60 m (Vaughan et al.
2004; available online at www-calipso.larc.nasa.gov/).
This makes it ideal for validation of retrievals from
passive sensors [see Stein et al. (2011) for a comparison
of MODIS ice cloud properties with CloudSat].
3. Space–time algorithm description
From here on we refer to any space-based measurement of a geophysical parameter, be it radiances, retrieved
clouds, surface, or layered thermodynamic properties,
simply as ‘‘measurement.’’ Moreover, we make the distinction between ‘‘measurement’’ and ‘‘observation’’ since
a geophysical parameter may not always be measured at
each observation opportunity in native instrument resolution (or FOV).
The space–time algorithm described here allows daily
measurements from any space-based instrument (polarorbiting or geostationary) to be gridded to an n8 3 n8
equal-angle grid (n . 0). A daily statistic is calculated
for each grid cell from which a time aggregate can be
generated to neutralize sampling differences among instrument measurements. The algorithm consists of two
phases, the first of which is the physical data resampling
phase, or ‘‘space gridding,’’ where measurements are
projected from their instrument observation grid to
a uniform equal-angle grid. All measurements are retained in this phase and clustered into nearest-neighbor
sets according to the specified gridcell size. (Note that
this is unlike the single value that is retained per grid
cell in more traditional gridding routines.) Second, the
statistical data reduction phase, or ‘‘time gridding,’’ is
where parameter-specific daily statistics are calculated
for each grid cell, or nearest-neighbor set. As soon as the
desired number of days is accumulated, a time-aggregate
statistical grid is calculated.
By dividing the gridding routine into two distinct
phases, opportunity is created for statistical data exploration, calculation of compound statistics (i.e., combining more than one measurement in calculation of
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descriptive statistics), or higher-order statistical moments. In this sense the space–time grid is first and foremost an analysis space with the time-aggregate grid as the
final output (or data product).
Below we discuss the space–time algorithm in more
detail and illustrate aspects of it by using MODIS CTP
retrievals (section 2a) as an algorithm application. Application to other geophysical parameters will be the
subject of future work.
a. Space gridding
One of the main advantages of gridding is data reduction. However, premature data reduction can severely
limit or misdirect research. Thus, an important first step
in any gridding routine is to carefully assess the research
requirements and define rules for filtering the measurements. For example, in this paper we demonstrate space–
time gridding for daytime high clouds retrieved from
near-nadir observations. The corresponding filtering criteria are sun zenith angle # 848 (daytime), CTP retrieval
#440 hPa (high clouds), and satellite zenith angle # 328
(near-nadir observations). Note that these criteria can be
provided from any coincident ancillary datasets; they
do not have to depend exclusively on the measurements.
Once the filters have been applied, only the measurements retained are gridded. This is an important consideration: from this step onward any opportunity for
inquiry that relies on measurements beyond those that
have been filtered by the criteria will be lost. However,
if a complete set of criteria is defined, then statistical
analysis of the data in gridded space will be more descriptive and meaningful.
Once filtered, the measurements are projected from
their native instrument resolution to a uniform gridded
resolution. The method developed for the space–time
algorithm is referred to as ‘‘snap-to-grid.’’ Each measurement is mapped to its nearest-neighbor (NN) grid
cell (sample size is at least one measurement). This differs from the standard approach where each grid cell is
assigned its NN measurement (sample size is one). The
set of measurements accumulated per grid cell makes
statistical data exploration possible. This is useful for
gaining insight that will ultimately inform phase two
of the algorithm (section 3b). Beyond the standard descriptive measures—such as mean, variance, mode, and
spread—one can gain insight into probable (common)
or even possible (rare) scenarios at this stage. Moreover,
knowledge of the sample distribution plus degree of linearity and entropy per grid cell can greatly enhance
gridded analysis.
The snap-to-grid routine is performed in three distinct steps. The geographic coordinate (x, y) in latitude–
longitude degrees (with fx 2 R: –90 , x 90g and fy 2 R:
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–180 , y , 180g) of each measurement is 1) converted
to a nonnegative real number set, r1 5 x 1 90, fr1 2 R:
0 , r1 , 180g and r2 5 y 1 180, fr2 2 R: 0 , r2 , 360g; 2)
adjusted according to the gridcell size (gsize) in units
(degrees) with fgsize 2 R: 0 , gsizeg, as follows r10 5
r1/gsize and r20 5 r2/gsize; and 3) rounded to the nearest
integer such that fr10 2 Z: 0 , r10 , 180/gsizeg and fr20 2 Z:
0 , r20 , 360/gsizeg (R and Z are the real and integer
number sets, respectively). Note that the output gridded
coordinate point (r 01 , r 02 ) may not be unique. Several
geographic coordinates may map onto the same gridded
coordinate. As such, a set of nearest-neighbor measurements is accumulated for each grid cell without any
distance calculation. This greatly simplifies the algorithm.
A single 3D grid is calculated per geophysical parameter per day. The grid has dimensions [nlat 3 nlon 3
nobs], where nlat and nlon indicate the latitude–
longitude dimensions respectively, and nobs the number of observations. The magnitude of nlat and nlon are
determined by the user-specified grid size; for example,
gsize 5 0.58 results in nlat 5 360 and nlon 5 720. The
magnitude of nobs varies on the one hand with gsize, and
on the other with source instrument spatial and temporal resolution. A coarser output grid resolution (larger
gsize values) results in a higher nobs value. Alternatively, a coarser input grid resolution (larger FOV areas)
results in a lower nobs value. Similarly, a higher frequency of measurements will result in a higher nobs
value. The magnitude of nobs can be greater than or
equal to the number of measurements (nmes) per grid
cell (nmes # nobs). The magnitude of nmes, in turn, is
simply the number of nonzero values in the gridcell
vector (with length nobs). The reason why nobs may in
some instances not be equal to nmes is that a geophysical
parameter is not always measured (retrieved) at each
instrument observation; for example, a cloud parameter
is not inferred for clear-sky conditions or a land surface
temperature is not retrieved in the presence of clouds.
A daily grid has a finite set of cells where nobs 5 0.
This may be the result of the applied criteria (e.g., cells
over polar nighttime regions will be empty if a daytime
criteria was specified), or simply due to limitations in
instrument coverage. A polar-orbiting instrument such
as MODIS samples roughly 70% of the globe per day,
but this depends on the swath width. The unsampled
portion is what leads to empty cells in a daily grid.
Note that no statistical calculations are made at this
phase of the space–time algorithm. It serves strictly as
a physical data resampling routine. The only data reduction that occurs at this phase is due to the filtering
routines. All data that pass the filters are resampled and
stored for statistical calculation during the next phase.
But all data that are filtered out are discarded, even the
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ancillary data are discarded. This simplifies data handling routines and speeds up enquiry during the next
phase. For the algorithm application we put forward in
this paper, 31 grids were computed, one for each day of
August 2009 at 18 3 18 resolution.
b. Time gridding
Statistical analysis is performed during this phase.
Where measurements from different times of the day
are accumulated per grid cell during phase one (e.g., as
a result of two consecutive orbits, or inclusion of measurements from both descending and ascending orbits),
they are statistically summarized into a single daily value
during phase two. The advantage of having a set of
measurements per grid cell should now become apparent; for instance, it allows the ability to calculate any
number of daily statistics, for example, mean, mode, and
standard deviation. Traditionally, daily gridded level 3
products contain no statistical information; they serve
only a physical data reduction purpose. Statistical analysis with daily level 3 products becomes possible only
once they are aggregated over time. We argue, however,
that premature data reduction has the potential to not
only limit scientific inquiry but also introduce small errors
that enlarge over time. Careful handling of statistical
data description from the outset has the potential to reduce data misrepresentation and enhance understanding
of observed trends and patterns.
In calculating the daily statistical grids, the dimension
of a space–time grid is initially reduced from [nlat 3
nlon 3 nobs] to [nlat 3 nlon]. However, the daily statistical grids stacked together form a second 3D grid
with dimensions [nlat 3 nlon 3 ndays] (with ndays as
the number of days). Once an aggregate time statistic
is calculated per cell, the final output grid has dimension [nlat 3 nlon]. In the area covered by the measurements, the time statistic will be calculated from at least
one daily statistic, that is, ndays $ 1. It remains to determine how the magnitude of ndays affects the final
result.
4. Algorithm application and sensitivity analysis
a. Weighted time average
The scope and flexibility of the space–time approach
is illustrated by calculating a compound weighted time
average of CTP. Note, however, that this is just an example since any descriptive statistic, model, or higherorder moment can be calculated for each daily grid cell
since nobs . 1 for each populated cell. The compound
weighted time average is provided by
å
CTPm 5
days
å
(% 3 CTPd )
å
(%)
5
days
days
nmes
3 CTPd
nobs
nmes
å nobs
days
,
(1)
where CTPm is the weighted time average of CTP and
CTPd the daily average of CTP. In this case, the nmes #
nobs since a cloud property may not always be inferred
for a given FOV (implying clear sky). This equation
calculates a weighted time average by combining daily
CTP averages with percentage cloud cover as defined by
the fraction nmes/nobs. This follows the line of argument that uncertainty in the final output is reduced when
the statistic is weighed by the fraction of occurrence. In
other words, in the example presented here the timeaggregate CTP average per grid cell is not just an average of averages but reflects the percentage cloud cover
such that the end result is dominated by CTP averages
from predominantly cloudy days (thus minimizing contribution from predominantly clear days). An alternative approach could be to weight the daily averages
by nmes only, which will give grid cells with a high
number of measurements (i.e., those in the center of
orbit tracks) a stronger weight in the time average. Far
from being prescriptive, Eq. (1) is merely an illustration
of the algorithm scope given the proposed gridding
configuration.
b. Sensitivity to sample size
Statistical analysis is sensitive to sample size; an average calculated from a small sample is more sensitive
(less robust) to outliers than those calculated from a
large sample. In gridded space it is important to maintain statistical robustness since the scale of geophysical
analysis makes it easy for small, localized errors to go
undetected initially but to accumulate over space and
time into questionable trends.
We characterize this sensitivity to sample size by evaluating the space–time algorithm response to minimum
sample size thresholds. In addition, we demonstrate how
sample size, and by implication the space–time product,
is affected by definitions of gridcell size, time period of
statistical aggregate, and viewing angle limitations.
Given a polar-orbiting instrument configuration, grid
cells on instrument swath edges (high viewing angles)
contain fewer observations than those at swath center
(near nadir). This can cause statistical errors that are
exaggerated when days are aggregated into months. For
example, a grid cell on the edge of an orbit swath for one
day could have nobs 5 3 and nmes 5 1. The same grid
cell could be in the center of an orbit swath for a different day, ending up with nobs 5 100 and nmes 5 12.
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TABLE 1. Mean and SD for the daytime high CTP difference between test 3 and tests 1, 2, and 4, respectively. Both global (908N, 1808;
908S, 1808) and regional (158N, 408E; 158S, 1008E) statistics are shown. The regional area corresponds to a part of the Indian Ocean
displayed in Fig. 1e. The tests are based on minimum threshold values for the number of observations (nobs) accumulated per grid cell
during the spatial gridding phase.
Test
1
2
3
4
A grid cell must
have at least:
One observation
10 observations
Lowest 16% of the monthly mean
observations for that cell
Lowest 3.5% of the monthly mean
observations for that cell
Global mean
difference 6SD
Regional mean
difference 6SD
nobs . 0
nobs . 10
nobs . mean(nobs) 2 [1 3 SD(nobs)]
1.44 617.51
1.48 617.93
0
2.07 621.46
2.09 620.09
0
nobs . mean(nobs) 2 [1.5 3 SD(nobs)]
0.62 611.55
1.22 615.78
Threshold
Given Eq. (1), the daily weighted average calculated
for the edge cell will make a larger contribution to the
monthly CTPm statistic than the center cell, even though
a single measurement determined the average. This is
addressed by setting a minimum limit for nobs to minimize the introduction of geographical misrepresentation
(i.e., when a large area is assumed to be homogenously
defined by a small isolated area). In single instrument
studies, repeated experimentation can lead investigators
to identify a static threshold for nobs, for example, 10.
However, with multi-instrument comparisons a single
static threshold can easily become meaningless since
nobs varies greatly depending on the value of gsize
and source instrument spatial and temporal resolution.
Thus we address two questions. What is the minimum
threshold for nobs to ensure a statistically robust sample
size for a grid cell? And, is there an objective method
with which to determine such a threshold?
Four different nobs thresholds are tested. They are
the following: 1) nobs . 0 (all grid cells are retained no
matter how low their nobs), 2) nobs . 10 (static threshold),
3) nobs . mean(nobs) 2 SD(nobs) [grid cells omitted with
nobs lower than 16%—half of one standard deviation
(SD)—of the mean nobs accumulated in a month], and
last 4) nobs . mean(nobs) 2 [1.5 3 SD(nobs)] (grid cells
omitted with nobs lower than 3.5%—half of 1.5 SD— of
the mean nobs accumulated in a month).
c. Results and discussion
The space–time algorithm is demonstrated in this
section using a specific application of CTP, namely
daytime (sun zenith angle # 848) high cloud CTP retrievals (CTP # 440 hPa) from near-nadir (viewing
angle # 328) Aqua/MODIS measurements (section 2a)
gridded to an equal-angle grid of 18 3 18 resolution and
time averaged over the period 1–31 August 2009. Daily
CTP averages are calculated that are then weighed
based on the percentage cloudiness and averaged for a
month according to Eq. (1). Even though this application is limited to daytime measurements that strictly
do not constitute a full ‘‘day’’ of satellite observations
(polar-orbiting sensors have both day- and nighttime
orbits), we maintain reference to ‘‘daily grids’’ for the
sake of simplicity. Note that all quantitative results
communicated in this section refer to this application,
unless otherwise specified.
On a single day, 288 files of 5 3 5 km MODIS measurements of potential CTP are generated. Each file
contains 270 3 406 observations. Because of the polarorbiting configuration of Aqua, the number of MODIS
observations per equal-angle 18 3 18 grid cell has a
strong latitudinal dependence; that is, the higher latitudes (.508) are sampled more frequently than the lower
latitudes (,508). For the application, a grid cell at (08N,
08E) has a total of 3603 daytime MODIS observations
for the month of August 2009, while a grid cell totals
4292 at (608N, 08E) and 12 180 at (808N, 08E). This could
raise a concern that differences in sample size may cause
higher degrees of smoothing in the poles than in the
lower latitudes. We contend that a limit on the maximum sample size can reduce this problem. Such a limit is
implemented in the space–time algorithm by restricting
calculation of statistics to a single day. As a result, a time
statistic then becomes the accumulation of single daily
statistics for a single day and therefore limits the exponential accumulation of observations in the poles that
can affect the statistical integrity of global results. Other
factors that limit the number of observations accumulated per grid cell per day are the filters applied at the
time of gridding, for example, time of day and viewing
angle restrictions.
In addition to addressing the maximum sample size,
limiting the minimum number of observations (nobs)
per grid cell per day is also a useful tactic to prevent
statistical instability. Three minimum threshold limits
were tested for nobs (Table 1), such that a daily average
was calculated for a grid cell if and only if the total observations on that day exceeded the threshold. With the
average number of MODIS observations per grid cell
per day about 280 (maximum 5 501) on a 18 3 18 grid,
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261
FIG. 1. The number of days (ndays) with daily averages for 1–31 Aug 2009 as a result of applying four different
thresholds to number of observations (see Table 1). (a) Test 1, (b) test 2, (c) test 3, and (d) test 4. White areas denote
no data due to the daytime filter applied. This applies to all subsequent figures.
a threshold of 10 is less than 1% of the nobs for most
cells. The AIRS operational L2 product, on the other
hand, has a coarser spatial resolution and averages 26
observations per cell per day (maximum 5 50) on the
same grid. A threshold of 10 is about 50% of the average
and will thus severely hinder daily global analysis by
removing too many cells from consideration. This
demonstrates that a static threshold can severely compromise multisensor comparisons. However, a dynamic
threshold that depends on a statistical relationship (e.g.,
tests 3 and 4 from Table 1) is independent of sensor
resolution and thus more useful.
The total number of days in a month where nobs
passed the threshold test is displayed for the three values
in Figs. 1a–d, respectively. The higher the threshold, the
fewer the available daily values; test 1 (that includes all
cells in calculation) has overall the highest values for
ndays, and test 3 (that filters out cells with the lowest
16% of nobs) overall the lowest ndays values. However,
variation in ndays is not limited to the threshold magnitude since ndays can vary as much as four days from
cell to cell across an orbit track in the low latitudes for
a single threshold. This is the result of orbital sampling
and shifting from day to day.
When compared to test 1, fewer than 27% of the cells
of test 2 register any difference (Figs. 1a,b). However,
given test 3, 53% of the cells have a difference of two or
more days and 36% of the cells given test 4. Although
the use of a minimum threshold reduces the number of
days with which a time statistic can be calculated, the
alternative of applying no threshold at all has a high
probability of introducing geophysical errors in the results. Conceptually, the scenario in which a small spatial
measurement (e.g., 5 km 3 5 km) determines the grid
value for a large uniform area of (e.g., 100 km 3 100 km)
should be avoided, and statistically, the reasons should
become apparent in the discussions below.
The weighted monthly CTP average (Fig. 2a) follows
the familiar geographic pattern also detected by Wylie and
Menzel (1999) and Wylie et al. (2005). The highest clouds
(.200 hPa) are found concentrated in the intertropical
convergence zone (ITCZ) with high clouds between 200
and 440 hPa in the midlatitude storm belts of the North
Atlantic, North Pacific, and Antarctic Oceans. No high
clouds were detected for the month of August 2009 in the
subtropical high pressure zones over the oceans and terrestrial subtropical deserts. These areas are typically characterized as having low cloud cover (Wylie et al. 2005).
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FIG. 2. Sensitivity to minimum number of observations. Weighted time averages of daytime high CTP for 1–31 Aug
2009 on a 18 3 18 grid with (a) test 1, (b) test 2, (c) test 3, and (d) test 4 (see Table 1). Differences between (e) tests 1
and 3, as well as (f) tests 1 and 4 are shown over the Indian Ocean in the region (58N, 408E)–(158S, 1408E). Black areas
denote absence of high clouds. This applies to all subsequent figures.
The monthly average difference between each test 2–4
and test 1 is displayed in Figs. 2b–d. Test 2 has the lowest
difference and test 3 the highest. Furthermore, it is clear
that applying a minimum threshold filter removes most
cells from the edges of orbit tracks (this is especially clear
in Figs. 2c,d). To illustrate how a nobs threshold can affect
the spatial coverage of a time statistic, daytime CTP averages were calculated for 81.6% of the grid cells with test
1 and 80.3% for test 3. Thus, although a minimum nobs
threshold removes cells from consideration, the effect on
the time-aggregate spatial coverage appears to be minimal.
Detailed differences in the time average for the four
thresholds can be seen for the Indian Ocean (58N, 408E)
to (158S, 1408E) in Figs. 2e,f. The difference of test 3 and
4 with test 1 are displayed as either (i) increased (,0),
(ii) decreased (.0), or (iii) remained the same (50) in
Figs. 2e,f. The diagonal stripes visible in Fig. 2f may be
a result of the shifting orbits from one day to the next.
Overall, though, the effect appears to be random and
localized. These results are for a month of observations
given a specific application. However, results may differ
with different time intervals, statistics, geophysical parameters, source instruments, and grid resolutions. Despite that, it remains desirable to retain as many of the
observations as possible, while removing outliers, to
ensure a robust sample size in the calculation of a time
statistic for each grid cell. Test 3 seems to remove too
many days from the monthly average calculation (Fig. 1).
Test 4 seems to be the most useful since it removes the
outliers (cells with the lowest 3.5% of nobs) without
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263
FIG. 3. Sensitivity to the definition of time in the calculation of a weighted time average. (a),(b) Total number of
MODIS level 2 observations (5 km 3 5 km) accumulated per 18 3 18 grid cell. (c),(d) Weighted average of daytime
high CTP on a 18 3 18 grid with sample size threshold 4 (see Table 1). (e),(f) Zoomed-in regional differences over the
Pacific of time averaged high CTP for 158N–158S and 1408–808W. All the figures on the left are for 1–31 Aug 2009, and
those on the right are for 1 Aug–1 Sep 2009.
severely compromising the total number of daily averages (Fig. 1). In addition, it is independent of instrument
spatial resolution unlike test 2.
As was demonstrated in Figs. 2b–d, the monthly cell
statistics can be sensitive to nobs thresholds that affect
the sample size. For test 3, the difference with test 1 is as
high as 288 hPa and globally averages 2 hPa (Table 1).
Other factors that affect sample size in the CTP application is gridcell size, viewing angle limitations, and
number of days in the time-aggregate statistic. The space–
time algorithm sensitivity to variations in these three
variables is discussed below.
The Aqua/MODIS has a 16-day repeat cycle. Given
the Gregorian calendar, a month ranges between 28 and
31 days and therefore does not readily coincide with this
cycle. We test here the sensitivity of monthly CTP gridded averages to two time aggregates: 32 days versus a
month (31 days in the case of August).
The total number of observations per 18 3 18 grid cell
is displayed for 31 (Fig. 3a) and 32 days (Fig. 3b), respectively. In the latter no orbit tracks are visible since
the time period coincides exactly with two Aqua repeat
cycles. This means that all grid cells in a latitude (zonal)
band are sampled equally, with a total observations per
grid cell that ranges from 4000 to 4500 in the low latitudes. This total number of observations per grid cell stays
near 4000 for 31 days (Fig. 3a). However, upon closer
inspection, orbital tracks are visible with a difference of up
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FIG. 4. Sensitivity to viewing angle. Weighted time average of daytime high CTP during 1–31 Aug 2009 on a 18 3 18
grid over the Pacific (308N, 1808W)–(308S, 808W) with threshold 4 applied (see Table 1) for (a) viewing angles # 328,
and (b) all viewing angles.
to 1000 (3500–4500) between adjacent grid cells. While it
is tempting to want to adapt a multiple of the 16-day cycle
for global statistics, the benefit is not apparent when the
weighted CTP average is considered in Figs. 3c,d; the
differences remain small with a global mean difference
20.22 hPa and standard deviation 17 hPa. These small
differences are more evident when the view is zoomed
in to a region over the eastern tropical Pacific (158N,
1408W)–(158S, 808W) (Figs. 3e,f). Of the 1891 grid cells in
this region, averages are calculated for the same number
of cells with only a few cells registering a change in average value. Note that the regional difference visible here
will drift from month to month because of satellite orbit
changes. For the sake of spatial coverage and perhaps an
ease of analysis description, Gregorian months are useful
statistical units that do not introduce any obvious artificial
features despite the initial uneven sampling.
The MODIS instrument has a scanning pattern of
6558. When we restrict our analysis to only those measurements from observations within 6328 of nadir, we
exclude a significant number of measurements. The rationale for excluding them is based on the fact that satellite observations at high viewing angles will be biased
toward larger cloud fractions; this is caused by the increase in pixel size with viewing angle. Just as in Fig. 3,
when the number of observations increases (as they do
when the viewing angle restriction is removed), the
spatial coverage increases and the time average decreases (because of larger sample sizes). This effect is
noticeable in Fig. 4. The weighted time average of CTP
is displayed for a region (308N, 1808W)–(308S, 808W)
with the near-nadir restriction (Fig. 4a) as well as for all
viewing angles (Fig. 4b). The former has zero values for
13.5% of all cells with a spatial average of the remaining
cells at 266 hPa. The latter, on the other hand, has
0 values for only 5% with a 250-hPa spatial average of
the remaining cells. We conclude that the gridding algorithm is highly sensitive to viewing angle restrictions.
Although the monthly CTP average of all retrievals
(with no view angle filtering) produces a smooth result
without the enhancement of features due to orbital sampling or gaps (e.g., as displayed in Fig. 4a), it is unrealistic
to assume that this could be applied to all instruments as
the scanning pattern varies greatly from instrument to instrument (e.g., AIRS has a scanning pattern of 648.958).
The goal with the space–time gridding algorithm is to
produce a tool with which to process retrievals from
any polar-orbiting instrument for easy multisensor
comparisons. A near-nadir criterion (viewing angle #
328) is not only scientifically conservative but also applicable to any cross-track scanning instrument. But
as demonstrated here, a limit of 328 may be too aggressive for CTP gridding alone (where cloud fraction is
irrelevant). A value .328 but less than the smallest
instrument viewing angle may serve a multisensor CTP
application better.
Finally, the sensitivity of the gridding algorithm is
tested to differences in grid size. The time average CTP
on a 18 3 18 grid is compared to that on a 28 3 28 grid
(Fig. 5). A larger grid cell will have a higher sample size,
so a degree of smoothing will occur. This is noticeable
when focusing the analysis on an eastern Pacific region
(308N, 1808)–(308S, 808W) (Figs. 5c,d). Small regional
features disappear when the grid size is enlarged. However, on a global scale many of the large features are insensitive to grid size. The most obvious sensitivity to the
grid size is the degree of spatial coverage. Most of the data
gaps in Fig. 5a disappear when the grid size is doubled in
Fig. 5b. Upon closer inspection, this has the additional
effect that new features are introduced on a coarser scale
that are not visible on a finer scale. We are in no position
to make recommendations as to the accuracy of one over
the other, but can merely conclude that globally gridded
statistics are very sensitive to grid size. Careful attention
should be paid to this when developing a test case or implementing a gridcell size for analysis in real time.
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265
FIG. 5. Sensitivity to gridcell size. Weighted time average of daytime high CTP for 1–31 Aug 2009 with threshold 4
applied (Table 1) and viewing angles # 328 on a (a) 18 3 18 grid and (b) 28 3 28 grid. Results are zoomed in to the
Pacific (308N, 1808)–(308S, 808W) in (c) 18 3 18 grid and (d) 28 3 28 grid.
We have demonstrated here some of the spatial and
temporal sensitivities of a new type of geophysical
space–time gridding algorithm with MODIS CTP retrievals as an example application. Any gridding criteria
or variable that causes the sample size to increase per
grid cell will result in a lower dynamic range of the
gridded measurement and smoother geophysical features in final product. The sensitivity of the algorithm to
sample size demonstrates that the application of
a general set of rules to the gridding of multiple geophysical parameters may not be appropriate. More
meaningful gridded statistical data can be generated
when a set of filtering criteria and gridding variables
unique to the science application and geophysical parameter of interest is developed. For different teams
to compare a given geophysical parameter in their
products to investigate similarities and differences, the
choices made in filtering the data must be clearly
stated. This will ensure that the observed spatial features and trends are less due to introduced errors and
more to the actual space–time properties. In the next
section we demonstrate how this gridding algorithm
can be applied to any number of instruments for a
multisensor comparison that is independent of instrument configuration.
5. Multisensor gridding application
In the final part of our study, we investigate the suitability of using the space–time algorithm for a multisensor comparison by calculating a gridded monthly
CTP average for four different polar-orbiting instruments: MODIS, AVHRR, AIRS, and CALIOP (section
2). This part of the experiment is limited to a visual
comparison as the objective is to evaluate the effectiveness of the algorithm for global comparisons. In a
future paper we will evaluate the strengths and weaknesses of various cloud retrieval algorithms and different polar-orbiting instruments on a uniform grid.
A weighted average of CTP [Eq. (1)] is calculated for
1–31 August 2009 on a 18 3 18 equal-angle grid. Test 4
was applied to remove grid cells with too few observations. The results in Fig. 6 represent the monthly average
of daytime high cloud CTP retrievals from near-nadir
observations (viewing angle # 328).
The intercomparison of cloud height retrievals from
different instruments has been the subject of a number
of studies (e.g., Wylie et al. 2005, Weisz et al. 2007). The
results displayed here reflect the widely known capabilities of the different instruments. The infrared instrument, AIRS, appears to be detecting more high clouds
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FIG. 6. Space–time gridded monthly averages of high CTP for four instruments: (a) operational MODIS (MYD06),
(b) PATMOS-x AVHRR, (c) operational AIRS level 2, and (d) CALIOP. The space–time gridding algorithm allows
multisensor comparisons. The results represent weighted time average of daytime high CTP for 1–31 Aug 2009 with
threshold 4 (Table 1) applied and viewing angles # 328 on a 18 3 18 grid.
than MODIS Collection 5 especially in the tropics.
AVHRR/PATMOS-x replicates the AIRS tropical high
cloud results but agrees more with MODIS in the midlatitudes and polar regions. Discrepancies between AIRS
and MODIS CTP averages depend not only on the
spectral region sampled but also on the spatial resolution of each instrument. The hyperspectral capabilities
of AIRS make it possible to capture small vertical features, whereas the high spatial capabilities of MODIS
make it possible to detect horizontal variability. The
lidar instrument, CALIOP, is very sensitive to the detection of optically thin clouds, but its coverage is limited
to a small number of grid cells in one month. CALIOP,
however, offers opportunities for validation of cloud results, despite its limited horizontal range.
These results illustrate the ease with which the uniform space–time gridding algorithm can be applied to
any number of instruments. A full gridded cloud retrieval
comparison of different instrument algorithms will follow
in future research.
6. Conclusions
The space–time gridding algorithm proposed in this
paper provides a method for combining and comparing
data from different space-based instruments on a common geographic coordinate system that is user defined.
Gridding requirements for a geophysical parameter
strongly depend on the research questions at hand.
Static generalized gridded data products, such as level 3,
from different sources may be incompatible and limited
in scope. Moreover, in the quest for broad application,
the creators of level 3 products may oversimplify geophysical data descriptions. With more than three decades of satellite data, the need for data combination
and continuity on a large scale has never been greater.
The algorithm proposed here breaks the problem of
gridding into two components: spatial data resampling
and subsequently temporal data reduction. The requirements for both components are user defined—from the
geophysical data filters to the grid size, type of statistic,
and length of time. The implementation of a gridding
algorithm, as opposed to using static gridded products for
analysis, has the advantage that any geophysical property
of interest at any level of processing can be gridded with
research-specific statistics in mind. This greatly simplifies
the gridding problem since key data reduction steps are
left up to the user to define. Additionally, this provides
the user with the flexibility to treat each geophysical parameter differently.
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In addition to the dynamic nature of the algorithm,
another novel characteristic is that all measurements
retained by the filtering criteria are resampled during
phase one. In other words, there is no spatial data reduction. Each grid cell contains a set of measurements
from which a daily statistic can be calculated. This is an
important consideration: the only type of data reduction
in the space–time algorithm is statistically based. Traditionally, daily gridded products are created by selecting a single value per grid cell, whether it is based on
a nearest neighbor or random location requirement.
However, with such an approach the daily products
serve a physical data reduction purpose. Statistical description is achieved only when daily grids are aggregated over time. This space–time algorithm, on the other
hand, allows statistical description on a daily basis. The
advantage of this approach is illustrated with the calculation of a weighted average. A cloud-top pressure
(CTP) average is calculated per grid cell per day and
weighed by the percentage cloudiness (number of
cloudy versus clear measurements per grid cell). As
a result, the time-aggregate average is dominated by the
CTP average from predominantly cloudy days. This
serves to reduce statistical uncertainty in the final output. Far from being prescriptive, this serves to demonstrate the scope of the space–time algorithm for the
calculation of compound statistics and error handling.
Four different threshold values for a minimum number of observations per grid cell are tested. We conclude
that a threshold that filters out those cells with fewer
than 3.5% (the lowest of a 1.5 standard deviation) of the
average number of observations per grid cell is rigorous
but not too aggressive to hinder daily global analysis.
Moreover it is instrument independent, which is an important consideration for multisensor comparisons.
The sensitivity of the space–time gridding algorithm is
investigated for gridding variables that affect sample
size, namely grid size, number of days, and viewing angle
restrictions. This is approach is illustrated by means
of an algorithm application using Aqua/MODIS cloud
retrievals (MYD06, collection 5). A time average is calculated for daytime high cloud retrievals from nearnadir observations for the period 1–31 August 2009.
Based on the results discussed in section 4, a number of
conclusions are reached. Regional features in the CTP
average are mostly artifacts of the cloud distribution
on single days rather than irregular orbital sampling.
Thus, any number of days (ndays) can be aggregated for
calculation of a time statistic. This is demonstrated
by comparing a time statistic calculated from a typical
Gregorian month definition (31 days) with one calculated from 32 days (coinciding with two Aqua platform
repeat cycles). The 31-day average did not introduce
obvious artificial features despite strong orbital sampling differences.
The sensitivity of the algorithm to sample size demonstrates that the application of a general set of rules to
the gridding of multiple geophysical parameters may not
be appropriate. We argue that more meaningful gridded
statistical data can be generated when a set of filtering
criteria (e.g., viewing angle limits) and gridding variables (e.g., gsize and ndays) are developed that are
unique to the science application and geophysical parameter at hand. This will ensure that the observed
spatial features and trends are due less to introduced
errors and more to the physical space–time properties.
Rather than producing static L3 gridded products, the
space–time algorithm described here provides analysis
flexibility with an opportunity for data exploration in
grid space. This could enhance the interpretation and
understanding of observed patterns and trends. Finally,
the conceptual and computational ease of the algorithm
lends it transparency to dynamically create gridded geophysical properties that are tailored to specific research
needs from any suite of space-based measurements.
Acknowledgments. This work is funded through NASA
Grant NNX11AK22G. The views, opinions, and findings
contained in this report are those of the author(s) and
should not be construed as an official National Oceanic
and Atmospheric Administration or U.S. government
position, policy, or decision.
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